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2023, Volume 44, Issue 1 publish date:January 01 2023
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Solid Mechanics
An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures
SU Cheng, LUO Junzhe, XU Zhi
2023, 44(1): 1-11.   doi: 10.21656/1000-0887.430116
Abstract(92) HTML(35) PDF(18)

Porous material structures have been widely used in civil engineering, mechanical engineering, aerospace engineering and other fields due to their high specific strength and specific stiffness. The stochastic response analysis of porous material structures under random excitations deserves more attention. The multiscale governing differential equations for porous material structures were derived based on the multiscale asymptotic-homogenization method (AHM), and the macroscale and microscale explicit time-domain expressions of structural responses were further established. On this basis, the statistical moments of dynamic responses of porous material structures under non-stationary random excitations were achieved with the explicit time-domain method (ETDM). The proposed method combines the advantages of the AHM for high-efficiency explicit formulation of macroscale and microscale dynamic responses of porous material structures and the benefits of the ETDM for fast analysis of non-stationary random vibration problems. A numerical example shows the computation accuracy and efficiency of the presented approach for non-stationary random vibration analysis of porous material structures.

Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States
ZHOU Shiqi, HOU Xiuhui, DENG Zichen
2023, 44(1): 12-24.   doi: 10.21656/1000-0887.430202
Abstract(53) HTML(21) PDF(28)

Based on the negative Poisson’s ratio effect of the re-entrant honeycomb, the finite element simulation of its buckling mechanical properties was carried out, and 2 buckling modes other than those of the traditional hexagonal honeycomb structures were obtained. The beam-column theory was applied to analyze the buckling strength and mechanism of the 2 buckling modes, where the equilibrium equations including the beam end bending moments and rotation angles were established. The stability equation was built through application of the buckling critical condition, and then the analytical expression of the buckling strength was obtained. The re-entrant honeycomb specimen was printed with the additive manufacturing technology, and its buckling performance was verified by experiments. The results show that, the buckling modes vary significantly under different biaxial loading conditions; the re-entrant honeycomb would buckle under biaxial tension due to the auxetic effect, being quite different from the traditional honeycomb structure; the typical buckling bifurcation phenomenon emerges in the analysis of the buckling failure surfaces under biaxial stress states. This research provides a significant guide for the study on the failure of re-entrant honeycomb structures due to instability, and the active application of this instability to achieve special mechanical properties.

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method
ZHANG Lei, ZHANG Wenming, WANG Lin, LI Shibin
2023, 44(1): 25-35.   doi: 10.21656/1000-0887.430097
Abstract(73) HTML(92) PDF(18)

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells.

Fluid Mechanics
The Mathematical Model and Research Progress of the Boundary Layer Flashback in Premixed Combustion
LI Wendong, ZHANG Wenpu
2023, 44(1): 36-51.   doi: 10.21656/1000-0887.430012
Abstract(50) HTML(38) PDF(15)

Flashback is a key problem influencing the normal operation of power equipment such as gas turbines. As one of the main mechanisms that cause flashback, the boundary layer flashback has an important effect on the design and operation of gas turbine combustors and other combustion devices. Since the critical gradient model for the boundary layer flashback was put forward by Lewis et al. in 1945, the theoretical models for the boundary layer flashback, such as the Peclet number model, the Damköhler number model and the flame angle theory, were developed one after another. However, these theoretical models still need improvements. Until now, the theoretical models for the boundary layer flashback are still in continuous development and modification. The history of the boundary layer flashback was reviewed, and the background, pertinence and shortcomings of the theoretical models were elucidated in the order of the model establishment time. In addition, the development status and research progress of the theoretical models for the boundary layer flashback in recent years were summarized, especially the progress made with new methods such as numerical simulation and statistical analysis. Further, the theoretical research direction and breakthrough points of the combustion boundary layer flashback at present and in the future were put forward.

Stokes Flow in Cylindrical Containers With Rotating Ends
WANG Gaping, LIU Jinghui
2023, 44(1): 52-60.   doi: 10.21656/1000-0887.430197
Abstract(113) HTML(82) PDF(39)

The Stokes flow in cylindrical containers with rotating ends was studied. Based on the characteristics of the flow, the problem was reduced to the eigenvalue and eigensolution problem of Hamiltonian dual equations with the axial coordinate simulated as the time scale. By means of the completeness of the symplectic eigensolution space and the adjoint symplectic orthogonality relationship between the eigensolutions, the expansion of the solution to the problem was obtained, and the numerical method for calculating the expansion coefficients was given. In the cases of one-end rotating, two-end rotating at the same or opposite angular velocity, the velocity and stress distributions of the flow in the cylindrical containers with different aspect ratios (of the length to the radius), were investigated. The velocity and stress distributions, and the characteristics of the flows under different boundary conditions were revealed.

Study on Discharge Coefficients of Drain Orifices in Closed Cavities
HU Renqiang, ZHANG Tao, LU Liuyun, XU Changyue
2023, 44(1): 61-69.   doi: 10.21656/1000-0887.430100
Abstract(49) HTML(23) PDF(11)

The discharge flow was numerically simulated to obtain discharge coefficients. The main factors influencing the discharge coefficients of orifices were studied by dimensional analysis, and the empirical fitting formulas for calculating discharge coefficients were given. The results show that, with a water head height less than 200 mm, the discharge coefficient decreases with the increase of the head height. With a water head height more than 200 mm, the discharge coefficient keeps stable around 0.61. The discharge coefficients with different thickness to diameter ratios show 2 different forms: the orifices with small thickness-diameter ratios show thin orifice flow characteristics, and the discharge coefficient is about 0.6; the orifices with big thickness to diameter ratios show thick orifice flow characteristics, and the discharge coefficient is about 0.8.

Numerical Investigation of Particle Focusing Patterns in Laminar Pipe Flow With High Reynolds Numbers
LIU Tangjing, WANG Qikun, ZOU He
2023, 44(1): 70-79.   doi: 10.21656/1000-0887.430075
Abstract(50) HTML(32) PDF(14)

The inertial focusing characteristics of particles in laminar flow pipes with high Re numbers were studied based on the “relative motion model”. In order to solve the problem of long pipes with high Re number flow, periodic boundary conditions were imposed on the inlet and outlet of the pipe. The research results show that the use of periodic boundary conditions can effectively reduce the computational, and the mechanical properties of particles in high Re flow can be calculated by using L=4D pipe. The difference from the low Re number is that as the Re number continues to increase,the lift force of the particles in the radial direction is no longer distributed as a parabola. The lift curve has a concave area between r+ =0.5 ~ 0.7, and there is a tendency for a new inertial focus point to appear in this section. By means of particles of a+ =1/17 for Re > 1 000, this new focus point position is solvable. In addition, in the analysis of the flow field, a secondary flow occurs around the particle, and its intensity gradually increases with the Re number and the closeness of the particle to the wall. The generation of the secondary flow affects the spatial distribution of the particle lift.

Applied Mathematics
Algorithm Research Based on the PDE Sensitivity Filter
MENG Huanli, ZHANG Qiliang, WANG Jie
2023, 44(1): 80-92.   doi: 10.21656/1000-0887.430064
Abstract(45) HTML(32) PDF(17)

The PDE sensitivity filter can eliminate the checkerboard patterns and numerical instability existing in the topology optimization results of continuum structures, and the essence of the PDE sensitivity filter is the Helmholtz partial differential equation with Neumann boundary conditions. To solve the large-scale PDE sensitivity filter problem, the conjugate gradient algorithm, the multigrid algorithm and the multigrid preconditioned conjugate gradient algorithm were used to solve the algebraic equations obtained by finite element analysis, and the effects of accuracy, filter radius and grid numbers on the efficiency of topology optimization were studied. The results show that, compared with the conjugate gradient algorithm and the multi-grid algorithm, the multi-grid preconditioned conjugate gradient algorithm has the least number of iterations and the shortest running time, which greatly improves the efficiency of topology optimization.

GPU Parallelization Computation of High-Dimensional Multi-Phase Separation in Complex Domains Based on the Corrected FPM
ZHEN Yujie, XU Kang, JIANG Tao, REN Jinlian
2023, 44(1): 93-104.   doi: 10.21656/1000-0887.430147
Abstract(60) HTML(56) PDF(11)

Based on the corrected finite pointset method (CFPM) with CPU-GPU heteroid parallelization (CFPM-GPU), a high-efficiency, accurate and fast parallel algorithm was developed for the high-dimensional phase separation phenomena governed by the multi-component Cahn-Hilliard (C-H) equation in complex domains. The proposed parallel algorithm with the CFPM-GPU was built in a process like: ① introduce the Wendland weight function into the discretization of the finite pointset method (FPM) scheme for the 1st/2nd spatial derivatives, based on the Taylor series and the weighted least square concept; ② use the above FPM scheme twice to approximate the 4th spatial derivative in the C-H equation, which is called the CFPM method; ③ for the first time establish an accelerating parallel algorithm for the CFPM with local matrices by means of a single GPU card based on the CUDA programming. Two benchmark problems of 2D radially and 3D spherically symmetric C-H equations were first solved to test the accuracy and high-efficiency of the proposed CFPM-GPU, and the acceleration ratio of the GPU parallelization to the single CPU computation is about 160. Subsequently, the proposed CFPM-GPU was used to predict the 2D/3D multi-phase separation phenomena in complex domains, and the prediction was compared with other numerical results. The numerical results show that, the proposed CFPM-GPU is valid and high-efficiency to simulate the 2D/3D multi-phase separation cases in complex domains.

A Well-Balanced HLL Scheme for Hyperbolic Conservation Systems With Source Terms
PENG Guoliang, WANG Zhongqi, ZHANG Junjie, REN Zeping, XIE Haiyan, DU Taijiao
2023, 44(1): 105-111.   doi: 10.21656/1000-0887.430084
Abstract(57) HTML(25) PDF(21)

A new finite volume scheme was proposed for hyperbolic conservation systems with source terms. The classical finite volume schemes could not accurately simulate the dynamic problems caused by the balance between flux terms and source terms. To deal with this problem, an approximate Riemann solver with source terms was designed in accordance with the classical HLL approximate Riemann solver. The well-balanced HLL scheme (WB-HLL) was obtained through modification of the flux calculation schemes for 1D Euler equations and ideal MHD equations with gravity source terms, and a proof for the well-balanced property of the new scheme was presented. Two numerical examples of 1D Euler equations and ideal MHD equations demonstrate that the proposed WB-HLL scheme has higher accuracy and faster convergence than the classical HLL ones.

Diffusive Regularization Inverse PINN Solutions to Discontinuous Problems
LIN Yunyun, ZHENG Supei, FENG Jianhu, JIN Fang
2023, 44(1): 112-122.   doi: 10.21656/1000-0887.430010
Abstract(63) HTML(55) PDF(25)

It is of great importance to numerically capture discontinuities for the numerical solutions to hyperbolic conservation laws equations. The PINN (physics-informed neural networks) was used to solve the forward problem of the hyperbolic conservation laws equations, with the diffusion term added, which is difficult to determine and needs to be obtained through high-cost trial calculation. To capture the discontinuous solutions and save calculation costs, the equation was regularized through addition of diffusive terms. Then the regularized equation was incorporated into the loss function, and the exact solutions or reference solutions to the conservation laws equations were used as the training set to learn the diffusion coefficients, and the solutions at different moments were predicted. Compared with that of the PINN method for solving forward problems, the resolution of discontinuous solutions was improved, and the trouble of massive trial calculation was avoided. Finally, the feasibility of the algorithm was verified by 1D and 2D numerical experiments. The numerical results show that, the new algorithm has better ability to capture discontinuities, produces no spurious oscillations and no screed phenomena. Additionally, the diffusive coefficients obtained with the new algorithm make a reference to construct the classic numerical scheme.

The PseudoExcitation Method and Its Industrial Applications in China and Abroad
LIN Jia-hao, ZHANG Ya-hui, ZHAO Yan
2017, 38(1): 1-31.   doi: 10.21656/1000-0887.370578
[Abstract](1333) [PDF 1039KB](1432)
Damage Identification for Bridge Structures Based on the Wavelet Neural Network Method
XIAO Shu-min, YAN Yun-ju, JIANG Bo-lan
2016, 37(2): 149-159.   doi: 10.3879/j.issn.1000-0887.2016.02.004
[Abstract](1283) [PDF 5386KB](745)
Uncertainty Quantification for System Identification Utilizing the Bayesian Theory and Its Recent Advances
YAN Wang-ji, CAO Shi-ze, REN Wei-xin.
2017, 38(1): 44-59.   doi: 10.21656/1000-0887.370571
[Abstract](1321) [PDF 647KB](965)
Some New Advances in the Probability Density Evolution Method
LI Jie, CHEN Jian-bing
2017, 38(1): 32-43.   doi: 10.21656/1000-0887.370336
[Abstract](1381) [PDF 683KB](2074)
Detached-Eddy Simulation of Flow Past Tandem Cylinders
ZHAO Wei-wen, WAN De-cheng
2016, 37(12): 1272-1281.   doi: 10.21656/1000-0887.370546
[Abstract](924) [PDF 3862KB](616)
Convergence Results on Heat Source for 2D Viscous Primitive Equations of Ocean Dynamics
LI Yuanfei
2020, 41(3): 339-352.   doi: 10.21656/1000-0887.400176
[Abstract](821) [FullText HTML](94) [PDF 405KB](299)
Simulation of Multi-Hydrofracture Horizontal Wells in Shale Based on the Extended Finite Element Method
CHEN Jun-bin, WEI Bo, XIE Qing, WANG Han-qing, LI Tao-tao, WANG Hao
2016, 37(1): 73-83.   doi: 10.3879/j.issn.1000-0887.2016.01.006
[Abstract](1124) [PDF 1871KB](689)
页岩储层水平井分段多簇压裂簇间距优选是压裂技术的关键,建立了水力压裂流固耦合数学模型,基于扩展有限单元法模拟多条裂缝的扩展过程,研究多条裂缝同时扩展的转向规律,以及应力干扰、水平主应力差、裂缝间距等因素与裂缝转向角度的关系.结果表明:应力干扰作用对裂缝宽度具有限制作用,单条裂缝张开宽度比两条裂缝的大;裂缝转角随应力差的减小而增大,随压裂时间的增加而增大.簇间距越小,应力干扰越强,转角越大,综合主缝均匀扩展、支撑剂填充以及复杂裂缝网络形成等条件,确定最优簇间距为30~40 m.多条裂缝同时扩展时,中间裂缝会受到两边裂缝的限制作用,簇间距越小,限制作用越强,裂缝发育时间越长,扩展速度越慢.
Progresses in the Study on Vibration Damping Properties of Novel Lightweight Composite Sandwich Structures
MA Li, YANG Jin-shui
2017, 38(4): 369-398.   doi: 10.21656/1000-0887.370328
[Abstract](1426) [PDF 6800KB](1193)
作为新一代先进轻质超强韧结构材料,复合材料格栅和点阵夹芯结构受到了国内外学者的广泛关注.目前关于该类结构材料的设计制备以及相关力学性能研究已取得了大量的研究成果.然而对该类结构振动阻尼性能的研究则处于起步阶段.该文综述了纤维增强树脂基复合材料简单层合结构以及各类夹芯结构振动阻尼性能的研究现状.首先阐述其阻尼机理, 然后分别概述了复合材料简单层合板的微观和宏观阻尼模型、复合材料粘弹性阻尼夹层结构和新型夹层结构的阻尼预报工作,最后总结归纳现有关于该类结构阻尼特性研究工作中已取得的成果和不足之处,并对其未来发展进行了展望.
Optimization of Multimodal Transport Paths for Refrigerated Containers Under Carbon Emission Restriction
LIU Song, SHAO Yiming, PENG Yong
2020, 41(2): 204-215.   doi: 10.21656/1000-0887.400159
[Abstract](1031) [FullText HTML](128) [PDF 1329KB](413)
Investigations of Self-Propulsion in Waves of Fully Appended ONR Tumblehome Model
WANG Jian-hua, WAN De-cheng
2016, 37(12): 1345-1358.   doi: 10.21656/1000-0887.370525
[Abstract](1362) [PDF 3993KB](560)
采用基于重叠网格技术的CFD方法数值研究了全附体ONRT船模在迎浪工况中自航的水动力特性.文中数值计算采用自主开发的面向船舶与海洋工程的CFD求解器naoe-FOAM-SJTU.自航计算中船体运动及螺旋桨转动等通过重叠网格技术完成,波浪环境则采用求解器中的三维数值造波和消波模块实现.计算中自航船模的螺旋桨转速通过静水自航数值计算得出,波浪工况计算采用东京2015 CFD会议中标准算例进行设置.数值计算结果,如船体运动、实时航速变化等,与试验数据进行了对比分析.此外,给出了数值预报的推力和扭矩系数,并且通过详细的流场信息来分析和解释了船模在波浪中自航过程中的水动力变化情况.数值预报结果同试验值吻合较好,说明采用当前结合重叠网格技术和CFD的数值方法可以很好地预报波浪中自航问题.
Study of Stress Field Near Interface Crack Tip of Double Dissimilar Orthotropic Composite Materials
LI Jun-lin, ZHANG Shao-qin, YANG Wei-yang
2008, 29(8): 947-953.  
[Abstract](3129) [PDF 460KB](38)
A study of double dissintilar orthotropic composite materials interfacial crack was made by constivcting new stress functions and employing the method of composite material complex.In the case that the characteristic equations' discriminants are all more than zero,the theoretical fonmula of the stress field and the displacement field near the mode Ⅰ interface crack tip,without oscillation and inter-embedding between the interfaces of the crack were delved.
Second Order Approximation Solution of Nonlinear Large Deflection Problem of Yongjiang Railway Bridge in Ningbo
CHIEN Wei-zang
2002, 23(5): 441-451.  
[Abstract](5785) [PDF 395KB](150)
The solution and computational aspects on nonlinear deflection of Yongjiang Railway Bridge in Ningbo were investigated.An approximate iteration algorithm on nonlinear governing equation was presented,and the obtained results show that,if altitude difference and span of the riverbanks are taken as 5 meters and 100 meters,respectively,the maximum gradient in the middle of the bridge exceeds 5%,much larger than maximum allowance gradient in railway design code.Therefor,a new solution scheme for decreasing gradient of the bridge is put forward,that is,the altitude difference between two riverbanks can be decreased to about 1/10 of the initial magnitude by building roadbeds with 0.5% gradient and 1 kilometer length at two riverbanks.As a direct result,the deflection gradient of the railway bridge is much reduced and the value is between 0.5%~0.6%.